A suspension eye of the type described at the beginning is known from German Auslegeschrift 2,658,358. This has a band of rubber-like material, which is passed through in its central region by crosspieces. The outer region of the band has an approximately annular rhombus-like form. Moreover, the band has two arcuately running slits, which form two suspension points and on which on the one hand a hook is hung which is fastened to the floor of the motor vehicle and on the other hand a further hook is hung which is fastened to the exhaust system. Embedded approximately in the center of the cross-section of the outer annular part of the band is a self-contained liner, which is elastically deformable in the plane of the band and tension-resistant and may consist of a steel wire or a spring steel strip. This liner likewise has a rhombus-like initial shape. When stressed, the band deforms together with the liner, the permissible spring excursion being limited by a stretched position of the tension-resistant liner in the sense of a stop. Consequently, a progressive characteristic of the band during deflection is aimed for. Both the band of elastomer material and the liner assume forces over the entire permissible range of movement with corresponding deflection of the exhaust system, and therefore act together from the outset. Consequently, it is indeed possible to achieve a certain progressivity. However, it is disadvantageous that, due to the tension-resistant design of the liner, that is the use of a to this extent rigid steel wire in the stretched form, a very abruptly occurring stop is formed, which limits any further rebound. In addition, the liner is arranged approximately in the center of the annular region of the band and consequently at a corresponding distance from the slit-shaped suspension points, the intermediate space being filled with elastomer material. These regions of the band are subjected to considerable compressive loading in the stretched position of the liner, because the liner is of tension-resistant design. Consequently, there is the risk of excessively stressing the elastomer material in these regions. When compressed, the liner is substantially free, apart from bending forces, and the corresponding forces are absorbed by crosspieces on the band. The crosspieces may conversely also form a stop with one another, in order to limit the compressing movement. The tension-resistantly designed liner, which may also consist of a steel rope, is thus itself not extensible and does not consist of resiliently compliant material. With its bending deformability, from the outset it in fact only reinforces the band of elastomer material and, moreover, represents an abruptly occurring stop at the end of the rebound movement of the band.